Tokyo/Formulation/3.AHL-experssing model

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<br>[[Tokyo/Works|Works top]]  0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]  1.[[Tokyo/Works/Formulation |Formulation]]  2.[[Tokyo/Works/Assay |Assay1]]  3.[[Tokyo/Works/Simulation |Simulation]]  4.[[Tokyo/Works/Assay2 |Assay2]]  5.[[Tokyo/Works/Future works |Future works]]
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<br>[[Tokyo/Works|Works top]]  0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]  '''1.[[Tokyo/Works/Formulation |Formulation]]'''  2.[[Tokyo/Works/Assay |Assay1]]  3.[[Tokyo/Works/Simulation |Simulation]]  4.[[Tokyo/Works/Assay2 |Assay2]]  5.[[Tokyo/Works/Future works |Future works]]
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<br><br>'''Assay1'''  [[Tokyo/Formulation/1.toggle model |Step1]]  [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]]  [[Tokyo/Formulation/3.AHL-experssing model|Step3]]  [[Tokyo/Formulation/4.population model|Step4]]  [[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step5]]
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<br><br>[[Tokyo/Formulation/1.toggle model |Step1]]  [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]]  [[Tokyo/Formulation/3.AHL-experssing model|Step3]]  [[Tokyo/Formulation/4.population model|Step4]]  [[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step5]]
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Revision as of 06:55, 25 October 2007


Works top  0.Hybrid promoter  1.Formulation  2.Assay1  3.Simulation  4.Assay2  5.Future works

Step1  Step2  Step3  Step4  Step5


The differential equaitons of the system considering AHL produced by E.coli themselves were given as


Ex 3-1
Table 3


These equations were normalized as follows:


Ex 3-2


In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as


Ex 3-3


By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as


Ex 3-4


Therefore, the phase plane of this system can be plotted as Fig● and the number of equilibrium points were decided by the value of the parameters:


Figure 3.1.A
Figure 3.1.B
Figure 3.1.C

Step.3 >> Step.4